Problem: $\int x^{-3}\,dx=$ $+C$
Answer: The integrand is of the form $x^n$ where $n\neq-1$, so we can use the reverse power rule: $\int x^n\,dx=\dfrac{x^{n+1}}{n+1}+C$ $\begin{aligned} \int x^{{-3}}\,dx&=\dfrac{x^{{-3}+1}}{{-3}+1}+C \\\\ &=-\dfrac12x^{-2}+C \end{aligned}$ In conclusion, $\int x^{-3}\,dx=-\dfrac12x^{-2}+C$